SAN FRANCISCO (AP) — Exactly one month from Election Day, Republican Mitt Romney and President Barack Obama are both declaring they will win a race for the White House that remains anything but clear. Their trails are crossing again in Ohio, the state that could decide the election, and signs of urgency are emerging from each campaign.

"I very much intend to win this election," Obama told donors in San Francisco Monday night. "But we're only going to do it if everybody is almost obsessive for the next 29 days."

Romney stood in a driving rain in Newport News, Va., his wet hair sticking to the side of his face, to join the kinds of die-hard supporters he needs for victory. "People wonder why it is I'm so confident we're going to win," he told them. "I'm confident because I see you here on a day like this. This is unbelievable."

Obama plans to rally support from students at Ohio State University on Tuesday, the last day for Ohioans to register to vote. Early voting is under way there and in many other states in one form or another.

Romney is set to campaign in Iowa and then Ohio, two of the nine contested states on the path to 270 electoral votes. Still riding high after a strong debate performance, Romney is expected to attend a midday rally in Van Meter, a small town 20 miles west of Des Moines. Tough-talking New Jersey Gov. Chris Christie is scheduled to join Romney for a night rally near Akron, Ohio.

Obama maintains more paths to victory, but polling shows a tightening race after more than 67 million people watched Romney shine in the Denver debate last week. The challenger's path to victory is extremely narrow, particularly without Ohio. No Republican has won the presidency without carrying the state.

The competitors pivot to Ohio after closing out different missions.

Obama capped a two-day California visit that took him from the cliffside mansions of Beverly Hills to the golden fields outside Bakersfield to downtown San Francisco. The trip was mainly about raising millions of campaign dollars.

Romney sought to burnish his credentials as a potential commander in chief with a foreign policy address before Virginia Military Institute cadets, asserting that Obama's efforts have been weak in the volatile Middle East and his leadership in world affairs lacking overall.

Obama's aides said the president was upbeat in private, well aware that he had to do better in next week's debate in New York, but steady and looking forward to another shot.

Based on the presumed outcome of the 41 non-battleground states and Washington, D.C., Obama enters the final period banking on 237 electoral votes. Romney is assured of 191.

On the road to 270, the battleground states account for the final 110 electoral votes: Ohio, Florida, Iowa, Nevada, Wisconsin, New Hampshire, Virginia, North Carolina and Colorado.

Both Democrats and Republicans say internal campaign surveys following last week's debate show Romney cut into the lead Obama had built up in many key battleground states. But they say Obama still has an advantage in most of them.

A lack of independent polling makes it difficult to know whether that's true. Romney pulled ahead of Obama, 49 to 45 percent nationally, among likely voters in a Pew Research Center poll conducted after the debate.

TV-watching voters in the toss-up states continued to get inundated with negative ads from both sides.

"He doesn't have anything to run on so he's running all of these ads, outspending us here in Ohio trying to basically call us liars," Republican vice presidential nominee Paul Ryan told WTOL, a TV station in Toledo, Ohio.

Ryan and Vice President Joe Biden debate Thursday in Kentucky.

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Peoples contributed from Newport News, Va. Associated Press writers David Espo and Julie Pace in Washington and Ann Sanner in Columbus, Ohio, contributed to this report.